Frictional Forces: Static and Kinetic

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  • čas přidán 1. 03. 2017
  • Newton's first law tells us that an object in motion will remain in motion, but we don't really see that on earth, do we? If you throw a ball, or push a hockey puck, these things do eventually stop. Why? To answer this we must learn about static and kinetic friction!
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Komentáře • 355

  • @AAG414
    @AAG414 Před 2 lety +240

    this guy carried me through sophomore year chemistry and now he's carrying me through junior year physics

  • @lordofmysteries6436
    @lordofmysteries6436 Před rokem +59

    I did a short experiment. I watched this video 2 times: yesterday night and tonight.
    Yesterday, I understood everything he said but couldn't get anything inside my head. So I used the whole day today to read the book and solved many maths related to frictions.
    Tonight as I watched this video again I was able to understand everything loud and clear😁. Thanks professor Dave

  • @ElixiricEssence
    @ElixiricEssence Před 4 lety +139

    This is like a crash course but nothing about it is too clumped. Perfect, straight-to-the-point, and easy. Will subscribe and listen to you religiously throughout my physics course. Thank you.

    • @Jai_ShriJagannath
      @Jai_ShriJagannath Před 2 lety +1

      czcams.com/video/DE6QvdAO9Qw/video.html
      Reason of why static friction is more than kinetic or dynamic friction

  • @Achievius
    @Achievius Před 2 lety +34

    Professor Dave, your videos got me through physics 1 and 2 in my post-bacc, and as I'm studying for the MCAT I found myself needing additional explanation. The jingle came to my mind and I knew exactly where to go. So thankful for you and your videos!

    • @carultch
      @carultch Před 2 lety +3

      I think of the formula for heat in terms of mass, temperature and specific heat, when I think of MCAT. Q=m*c*∆T

    • @Metamor-phosis
      @Metamor-phosis Před 2 lety

      the jingle lol

  • @kera8378
    @kera8378 Před 5 lety +519

    Is it sad or impressive Dave can teach in 5 minutes what my professor can’t in 3 3 hour class periods?

    • @Lucky10279
      @Lucky10279 Před 4 lety +28

      Both. Impressive for Dave but sad for your professor and you guys. I'm in the same boat with my professor. His lectures are really disorganized. I was getting a little scared that I was getting confused so early in the semester, especially when I'm way ahead of the math requirements. Watching just a few of Dave's videos and I feel much more confident. I've learned more from from short CZcams videos than from 2 hour lectures.

    • @julianader739
      @julianader739 Před 4 lety +1

      YESSSSSSSSSSSSSSSSSSSSS

    • @blinkbubs3994
      @blinkbubs3994 Před 4 lety +3

      dude thats literally what happened to me in class. 3 hour class, dont understand much. i watch this, and it makes a lot of sense.

    • @Sasukej2004
      @Sasukej2004 Před 4 lety +3

      @Learn First very true, they want you to know how to do problems and smart students will read about it more at home

    • @unknownbeing8222
      @unknownbeing8222 Před 4 lety +5

      Am i the only kid watching this...

  • @andresjr.baybay2555
    @andresjr.baybay2555 Před rokem +8

    thanks a lot bro. this new subscriber is from the Philippines, the way you deliver the topic is so smooth, wonderful and easy to understand. thanks a lot. static & kinetic friction topic. great!

  • @stovegamesgames6917
    @stovegamesgames6917 Před 4 lety +15

    I swear without this video I would be super lost in my physics class

  • @alyssaboudreau3410
    @alyssaboudreau3410 Před 3 lety +20

    Unfortunately, my prof doesn't teach anything... so I am very thankful for your videos with visual aids! I hope you keep making more!!! Yours are by far the best on youtube! :)

    • @lemondrop8203
      @lemondrop8203 Před 2 lety +2

      You can't listen, that's why

    • @AXbcyz
      @AXbcyz Před 10 měsíci

      @@lemondrop8203someone’s never experienced a bad teacher

  • @kumpulanfoto1928
    @kumpulanfoto1928 Před rokem

    Thanks,dave. At this current time, i have a hard time learning about frictional force in orthodontic. And ur explanation makes me a little bit confidence. I understand the first 5:30 minutes,the rest remains a question for me. Thx

  • @AqibAli-hd7xp
    @AqibAli-hd7xp Před 4 lety +1

    thank you dave my physics teacher didn't explain in this way as you explained . thank you very much

  • @tridevjha255
    @tridevjha255 Před 2 lety +1

    This Guy explained these concepts in just 8 minutes which I am Trying to understand from 2 weeks

  • @lianethlozano8237
    @lianethlozano8237 Před 4 lety +6

    Your videos are so helpful, thank you so much!

  • @newtube553
    @newtube553 Před 4 lety +6

    Lots of new ideas thank you . It's relevant in my study

  • @meliksahyorulmazlar9742
    @meliksahyorulmazlar9742 Před 4 lety +2

    Thanks for helping Dave

  • @elfigahleitner4845
    @elfigahleitner4845 Před 6 lety +47

    thank you so much for sharing your knowledge with the world :D! now it all makes sense :)!!

  • @a4q2020
    @a4q2020 Před 2 lety +2

    We could see how much effort you put into creating a video.
    Super.👍
    We A4Q team with your growth.
    Full support 💪

  • @pubuduweerakoon7174
    @pubuduweerakoon7174 Před 5 lety +1

    Concepts are simply built...Thanks Sir..

  • @SifulIslam-jo7oe
    @SifulIslam-jo7oe Před 7 měsíci

    This is my first video of yours and I subscribed as soon as I saw it at a glance 😊

  • @krishnanandtiwari2023
    @krishnanandtiwari2023 Před rokem +1

    NOW THIS IS CLEAR THANKS PROFESSOR

  • @humaidalsuwaidi7359
    @humaidalsuwaidi7359 Před 4 lety +8

    Thank you, You’ve helped me understand the difference between the frictions.

  • @sethmanning6493
    @sethmanning6493 Před 2 lety +5

    7:05 aren't the x & y components mg*csc(theta) and mg*sec(theta) respectively? The trig here isn't checking out for me.
    ? to denote x-component of mg
    sin(theta) = mg/?
    ?*sin(theta) = mg
    ? = mg/sin(theta)
    ? = mg*csc(theta)

  • @lovelykids9785
    @lovelykids9785 Před rokem

    Super! You made the subject simple! Thanks

  • @akila.s6856
    @akila.s6856 Před 3 lety +1

    Wow..ur teaching is superb with practical learning

  • @kipguthrie2490
    @kipguthrie2490 Před 5 lety +8

    exactly what i needed before my test! thanks!

  • @IgnitedIce81
    @IgnitedIce81 Před 5 lety +7

    Thank you so much, I was stuck on a question and this video helped me a lot!

    • @Jai_ShriJagannath
      @Jai_ShriJagannath Před 2 lety

      czcams.com/video/DE6QvdAO9Qw/video.html
      Reason of why static friction is more than kinetic or dynamic friction

  • @magdalenakamecka1666
    @magdalenakamecka1666 Před 4 lety +2

    i think there is an error in checking comprehension. if the object is at rest, we wont know whether it moves unless we look at the static friction coefficient (as opposed to kinetic friction as stated)

  • @Tony-wo6rl
    @Tony-wo6rl Před 4 lety +16

    thank you so much! you saved a university newbie!

  • @danielgrezda3339
    @danielgrezda3339 Před 2 lety +3

    1:31 "This attractive interaction can hinder motion to some degree" This can easily be taken out of context.

  • @VAISANAN373
    @VAISANAN373 Před 4 lety +1

    Thank you. It helped a lot .

  • @henrylopez3014
    @henrylopez3014 Před 3 lety +2

    thank you man, i am teaching my nephew vectors and this video helps a lot to illustrate parts of the whole idea. thank you.

    • @Jai_ShriJagannath
      @Jai_ShriJagannath Před 2 lety

      czcams.com/video/DE6QvdAO9Qw/video.html
      Reason of why static friction is more than kinetic or dynamic friction

  • @user-hv6ef9ie1g
    @user-hv6ef9ie1g Před 6 měsíci +2

    6:54 I wonder if the Fnet=mgcos(theta)-Fsf resulted in a negative number (meaning the Fsf is greater than the mgcos), then what will happen? Will the box stay at rest or will the box move upwards? Depending on the context though, i'd guess the box would remain at rest.

  • @stevewalby1749
    @stevewalby1749 Před 3 lety

    Great explanation - thanks

  • @lovelyroseacyapat6639
    @lovelyroseacyapat6639 Před 2 lety +1

    thank you i really understand friction so easy

  • @Ash_2772
    @Ash_2772 Před 2 lety

    I was in tension abt tomorrow's exam but your intro made me free and calm

  • @rhiannonlarsen5805
    @rhiannonlarsen5805 Před 5 lety

    Great explanations!!

  • @HARIHMS
    @HARIHMS Před 4 lety +3

    Professor please make a video on tension it is an important topic please make it I love your teachings

  • @hala1909
    @hala1909 Před 2 lety

    Thank you for illustrating perfectly

  • @hdadam203
    @hdadam203 Před 3 lety +2

    Thank you man, you nailed it. My teacher can’t even explain it clearly 🙄

  • @maevamiranda1828
    @maevamiranda1828 Před 3 lety

    Wow thanks alot ,it was really well explained

  • @neurodivergentsophie8411
    @neurodivergentsophie8411 Před 4 lety +6

    Professor Dave, I have a question! If friction is caused by forces of attraction between atoms on a molecular, and electrostatic attraction is one of of these forces of attraction. Does this mean that friction can change based on the charge of the object?

    • @qriosiumi2455
      @qriosiumi2455 Před rokem

      Is it specified that the attraction is really electrostatic?

  • @iXRisesz
    @iXRisesz Před 3 lety +1

    Subbed not only because useful information but because Subaru 😎

  • @ghrmaykibreab2178
    @ghrmaykibreab2178 Před 8 měsíci

    thank you for explaining clearly

  • @niceguy4801
    @niceguy4801 Před 3 lety

    Thankyou Professor Dave!

  • @kyle_360
    @kyle_360 Před 2 lety

    Bruh, how does this guy manage to learn something that is hard to explain in such ease and how long did it took for him to learn this stuff?

  • @haafilah253
    @haafilah253 Před 2 lety

    when the mass of an object increases the normal & frictional force increases do the static force increases as well?

  • @revanthalexkumar7597
    @revanthalexkumar7597 Před 3 lety +1

    Very precise

  • @emanalnashami3835
    @emanalnashami3835 Před 4 lety +1

    thanks, really helped

  • @BonjourMelanie
    @BonjourMelanie Před 7 lety +14

    Hello! In the comprehension check you use Fnet= mg sin theta - Ff, I am confused as to why you are using subtraction instead of addition.
    Thanks!

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  Před 7 lety +10

      it's true, it could be addition as long as you then make the frictional force negative, we just need opposite signs on the two horizontal forces as they are in opposite directions. in the end, as long as the signs make sense you're all good!

    • @pubuduweerakoon7174
      @pubuduweerakoon7174 Před 5 lety +1

      There is no certain direction for a frictional force to be acted. It is always resistive to a motion or to an attempt to the motion. When the block moves or tends to move down, frictional force would act up the incline. When the block moves or tends to move up, the frictional force would act down the incline. Thanks.

    • @Diamondlight04
      @Diamondlight04 Před 5 lety +1

      Is it safe to assume then, that in problems like these as long as the box is going downwards the frictional force will be negative ?

    • @phamdung3884
      @phamdung3884 Před 4 lety +1

      KB yes. It’s in the opposite direction of the motion so it’ll be negative.

  • @stevesanders3992
    @stevesanders3992 Před rokem

    If I wind a rope around a spool body, how many winds do I need to get a frictional grab where it can not slip? Thanks

  • @akshay5295
    @akshay5295 Před rokem

    @professor_dave_explains do you still stands by the statement that rougher surfaces have more friction?

  • @AqibAli-hd7xp
    @AqibAli-hd7xp Před 3 lety

    Nice explained.

  • @ntandondlovu4176
    @ntandondlovu4176 Před 2 lety

    which is correct, is it @6.31 : net force = kinetic friction + mg sin theta or @6.53 : net force = mg sin theta - kinetic friction
    confused help

  • @gioivanmijares7787
    @gioivanmijares7787 Před 5 lety +3

    Hello. I'm just confuse because I read the book named "Conceptual Physics" that says that Increasing contact points doesn't add to the friction. Can someone clarify thanks

    • @CartwheelPig
      @CartwheelPig Před 3 lety +1

      I'm not positive but I think it has more to do with the force of gravity on the contact points than the points themselves. If I have two boxes of the same size on the ground (therefore both boxes have equal contact points with the ground) and one weighs more, the normal force will be greater, and therefore the frictional force will also be greater.

  • @sebastianrojas5419
    @sebastianrojas5419 Před 8 měsíci

    This model works very well for hard surfaces. I wonder how the contact area and other factors start to be important when analyzing friction in deformable surfaces like rubber or human tissue? Would be interesting to know :)

  • @kazuhiramiller7752
    @kazuhiramiller7752 Před 11 měsíci +1

    But Sir how we will know what is the value of cos 35° and sin 35°?

  • @easyfacts6745
    @easyfacts6745 Před 4 lety

    now I understood the difference between static and kinetic. whoa!!

  • @abdulbayesusmany6184
    @abdulbayesusmany6184 Před 3 lety

    very helpful!

  • @dankydoodle3089
    @dankydoodle3089 Před 5 lety +1

    I have a question: Why is static friction used to walk forward? I know our foot pushes backwards, and the friction lets us go forward, but i thought that static friction only resisted the initiation of motion. Is there an another definition for static friction or am i just not understanding this concept correctly?

    • @carultch
      @carultch Před 2 lety +2

      It is only locally that static friction opposes the initiation of motion. Locally at the point of contact between two objects. The static friction in this example, is what stops your foot from moving backwards as you push it backwards while trying to walk. If you were on a truly frictionless surface, your foot would slide backwards and you would run in place if you tried to walk.
      Think of the Earth's surface a "work mirror". You push backward on the ground, by pushing your foot backward while it is in contact with the ground. By Newton's third law, the ground also pushes forward on your foot with an equal and opposite force. The force on the ground by your foot, cannot practically do any measurable amount of work on the Earth, because of the Earth's inertia is so large that its motion due to this force is immeasurably small. Instead what happens, is that the ground reflects this force back to you, through its third law pair of this force, as the ground applies a forward force to your foot, while your body moves.

  • @Rayan-jx3sn
    @Rayan-jx3sn Před 3 lety

    Thank you so much sir!!!!

  • @evapace43
    @evapace43 Před rokem

    I love you and your channel so much dude

  • @ppmp9937
    @ppmp9937 Před 3 lety

    Thank you sir!

  • @Lucky10279
    @Lucky10279 Před 4 lety

    So why does static friction have a maximum value? What causes it to suddenly stop increasing?

  • @nicolejaja270
    @nicolejaja270 Před 4 lety

    What If I have a problem where it's supposed to be solved by work kinetic theorem AND THEY JUST GIVE THE FRICTION, MASS AND DISTANCE AND ASK ME TO FIND THE INITIAL VELOCITY. WHAT I NEED TO DO?

  • @georgemwanza7466
    @georgemwanza7466 Před 3 lety +1

    Sir why are we subtracting friction forces from mgsin35 to have friction net force instead of adding to satisfy the static condition of forces in the x- axis

    • @f-22raptor25
      @f-22raptor25 Před 3 lety +1

      Friction is in another direction it must be taken away

  • @noyes5178
    @noyes5178 Před 2 lety

    Why is coefficient of friction = the angle the object is sliding at?
    Isn't it determined by the surfaces smoothness?

  • @afiyaparveen8288
    @afiyaparveen8288 Před 5 lety +1

    Amazing.

  • @vincent90s80
    @vincent90s80 Před 3 lety

    Thank you 💜

  • @akashbehera1465
    @akashbehera1465 Před 4 lety

    most welcome Dave

  • @whhy9708
    @whhy9708 Před 3 lety +1

    Oh sir...
    Thanks for saving me ... Actually i love physics but the concept of cofficent "i was unable to understand 8t properly but after you video .. everythings is clear...
    Thanks sir! !!!!

    • @carultch
      @carultch Před 2 lety +1

      Coefficient just means a number multiplied by another number. Like in y = A*x^2 + B*x + C, the A and B are examples of coefficients.

  • @inetuser424
    @inetuser424 Před 3 lety

    COOL SUBARU CLIP! really piqued my interest. are you a subaru driver, dave?????

  • @NewToneProducer
    @NewToneProducer Před 3 lety +1

    FYI for people watching this, Fstatic is NOT always greater than Fkinetic. The magnitude of Fstatic depends on how much other force acting parallel to the surface exists. Fstatic can be as much as 0 N if there are no forces trying to slide the object across the surface.

    • @carultch
      @carultch Před 2 lety

      It is mu_static that is always greater than mu_kinetic. N*mu_static sets the upper limit for how large Fstatic can be. Whereas N*mu_kinetic sets what the friction force will be, in the event that there is existing sliding veocity.

  • @taihatranduc8613
    @taihatranduc8613 Před 3 lety

    thank you, sir. You are so gooooood...

  • @Nikkizsche
    @Nikkizsche Před 4 lety +1

    Helpful :) thank you.

  • @sumyyarahman1742
    @sumyyarahman1742 Před rokem

    Many thanks.

  • @FagbeluEmmanuel
    @FagbeluEmmanuel Před 5 měsíci

    Does the net force depend on the direction of motion if the body or is it always Fnet= mgsin@ + Ff

  • @ryanpiotr1929
    @ryanpiotr1929 Před 10 měsíci

    But why does static friction push back exactly as much as I push the object? And why is there a maximum? Why is dynamic friction always weaker?

  • @joelfernando6207
    @joelfernando6207 Před 5 lety

    Lot of thanks

  • @aschetos
    @aschetos Před 2 měsíci

    Very good

  • @jononeep4977
    @jononeep4977 Před 5 lety

    Thanks for explaining Dave but what if there is no applied force and there is a friction force? Does that mean the object will move the other way

  • @wanuradhaw
    @wanuradhaw Před 3 lety

    Thank you professor

  • @IamPazan
    @IamPazan Před 5 měsíci

    Professor Dave Explains , The Classic Vintage Intro.

  • @dollmarya5931
    @dollmarya5931 Před 10 měsíci

    The best intro ever seen😄👍🏻

  • @nandagopanms1528
    @nandagopanms1528 Před 6 lety

    Can you please add a video about free body diagram in detail

  • @05afnanabdullah87
    @05afnanabdullah87 Před 7 lety +6

    Can work done against non conservative forces get stored in the form of potential energy?

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  Před 7 lety +5

      oh man, good question. i can't think of how that would work but i'm sure there must be some example.

    • @05afnanabdullah87
      @05afnanabdullah87 Před 7 lety +1

      Professor Dave Explains​ the Induced magnetic field in a coil is a non conservative field. Still work is stored in the form of magnetic potential energy. Is it the same thing? Thanks :)

    • @pubuduweerakoon7174
      @pubuduweerakoon7174 Před 5 lety +1

      Can't. That work will be wasted mostly as heat. This is what the meaning of "nonconservative"

    • @pubuduweerakoon7174
      @pubuduweerakoon7174 Před 5 lety

      It is very clear that, any conservative force must be accompanied with a kind of potential energy. But Nonconservative forces are not. By the way, conservative force is defined by the equation of F = dU/dx. Where dU is the differential of potential energy. Work done against a conservative force will result an increase in the kind of potential energy and vise versa. Work done by a nonconservative force will definitely waste the energy which is not reversible as dU. Thank you Sir.

  • @lime4328
    @lime4328 Před rokem

    I LOVE U PROF. DAVE !!!

  • @xyliahvortex661
    @xyliahvortex661 Před 3 lety

    Thanks!

  • @tujidititoogi
    @tujidititoogi Před 2 měsíci +1

    highly recommended☺

  • @remitoinfinity
    @remitoinfinity Před 11 měsíci

    May I have a question. At 1:27 you said the interaction between atoms in the object and atoms in the surface is an attractive interaction. But shouldn't it be repulsive instead? Because the interaction here is between electrons of the object's atoms and electrons of the surface's atoms, both are negatively charged, so they should repel each other instead of attract, right?
    And if they repel each other, logically this interaction should help facilitate the motion by pushing the two surfaces away from each other. But in fact, motion is hindered. Could you explain how it works?

    • @kazuhiramiller7752
      @kazuhiramiller7752 Před 11 měsíci +1

      Atoms that are stable have no net charge.
      The atom consists of protons as well which cancels the effect of negatively charged electrons. In an atom (which is not an ion) the number of protons and electrons are equal and both of them have the same charge.(i.e charge in a single proton= charge in a single electron) . ( This is 100% true)
      But the thing is that, even if two charged bodies are interacting still friction will act upon them. Considering that the bodies are big(big enough that we can see them). This is classical physics. Here we deal with objects that are not very small. (Although I am not 100% sure about this one)

  • @muchingadaka81
    @muchingadaka81 Před 4 lety

    Could you talk about Law frame of inertia

  • @nasifulhuda31
    @nasifulhuda31 Před 3 lety

    Thank you

  • @lovelyroy2891
    @lovelyroy2891 Před 18 dny

    Can anyone explain why add? 6:27

  • @jamespoda5621
    @jamespoda5621 Před 4 lety

    wow thank you you the simply the best

  • @JJherne
    @JJherne Před 3 lety

    Question - how can F=ma if F is a variable? In a previous video we see how a puck requires very little force to move across ice, but put that same puck on sandpaper and it'll require more force to move it in the same manner. Is it just that when dealing with additional forces such as friction, "F=ma" becomes Fnet=ma?

    • @carultch
      @carultch Před 2 lety +2

      It always is Fnet = m*a. We just get away with omitting the subscript of "net" when we are only dealing with one force that makes a difference in the object's acceleration.
      When the puck moves across the ice, there are two significant forces which you ignored completely. Namely, the weight of the puck, and the normal force of the ice pushing upward on the puck. These forces add up to zero, by the nature of the normal force, since the normal force will be as large as necessary within the strength of the materials, to prevent penetration. Because these forces add up to zero, they cancel out of the equation of Fnet=m*a.

    • @kazuhiramiller7752
      @kazuhiramiller7752 Před 11 měsíci +1

      Definition of force is that:-
      F=ma

  • @zrzx999
    @zrzx999 Před 7 měsíci

    But isnt friction also depends on the size of the base of the object? A bigger box will touch more things on the floor a small box will touch less, regardless of the mass.
    Someone explain

  • @euyoooo
    @euyoooo Před 7 lety +1

    Hi Dave, It has been like 10 years since I did trigonometry, so pleaase forgive my ignorance! How did you come up with mg Cos TH and mg Sin TH?

    • @ProfessorDaveExplains
      @ProfessorDaveExplains  Před 7 lety +7

      SOHCAHTOA! you have to make a triangle and rearrange the definitions of the trig functions. i go over it in one of the earlier tutorials in the classical physics playlist, i think the one on vectors. but i will go over it in much more depth in my upcoming trigonometry tutorials!

    • @yousseftakla2182
      @yousseftakla2182 Před 7 lety +1

      Thank you!

  • @mohammadedressrahimi1382

    I really appreciate you tnx so much

  • @evanjenelnesbitt1140
    @evanjenelnesbitt1140 Před 4 lety +2

    In the comprehension check, if the block begins at rest, why don’t we account for static friction before kinetic?

  • @kvlx2826
    @kvlx2826 Před 5 měsíci

    anyone know why the kinetic frictional force in the comprehension is being multiplied with the y component of gravity as opposed to the x component?

    • @HeldanaSeifu
      @HeldanaSeifu Před 4 měsíci

      I think it's bc we r finding the acceleration and as the box accelerates the weight cos opp or slow it that's my understanding

  • @sonalimahajan8960
    @sonalimahajan8960 Před 4 lety

    Friction does not, depends upon mass,and contact area? How it is possible because as mass and contact area increses their is more adhesion between surfaces of two objects, so more force is required and so equal and opposite reverse friction force operate. Kindly clear my doubt

    • @carultch
      @carultch Před 2 lety

      The unitless friction coefficient is independent of mass and surface area. It depends on the identities of the two surfaces, the conditions of the two surfaces, and whether the friction is static or kinetic.
      From a first order overview of friction, it is independent of surface area. The surface area ends up "cancelling out" of the equation.
      The friction force itself, will indirectly depend on mass, because it depends on the normal force, which is usually a reaction force to the object's weight, in some form or another.

  • @jordanjohn2168
    @jordanjohn2168 Před 3 lety +3

    How did you get so good at solving, what did you do when you were a student... I want tipsssss as many as the s' s i put

    • @kazuhiramiller7752
      @kazuhiramiller7752 Před 11 měsíci +1

      I think he has used calculator. How can someone know the values of sin 35 and cos 35 and use their decimal values in an equation? The equation becomes long and we have multiply big numbers. I think giving angles like 30,45 or 60 is good because their values are easy to work with at the time of calculation.